cp's OEIS Frontend

A334445 Decimal expansion of Product_{k>=1} (1 + 1/A002144(k)^4).

%I A334445 #11 Jun 27 2020 11:53:16
%S A334445 1,0,0,1,6,4,9,6,6,4,0,3,3,0,0,0,4,2,5,3,7,8,5,7,8,0,7,1,9,2,9,3,9,0,
%T A334445 8,8,8,2,7,3,9,8,4,4,0,4,3,8,6,6,9,9,3,0,0,0,8,9,8,3,7,4,0,9,6,6,7,9,
%U A334445 2,0,4,8,0,8,2,3,6,3,4,3,4,4,1,9,2,9,8,6,5,3,3,1,1,7,8,9,9,7,0,6,1,5,7,0,9
%N A334445 Decimal expansion of Product_{k>=1} (1 + 1/A002144(k)^4).
%C A334445 In general, for s>1, Product_{k>=1} (1 + 1/A002144(k)^s)/(1 - 1/A002144(k)^s) = (zeta(s, 1/4) - zeta(s, 3/4)) * zeta(s) / (2^s * (2^s + 1) * zeta(2*s)).
%D A334445 B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
%H A334445 Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/landau.ps">Zeta function expansions of some classical constants</a>, Feb 18 1996, p. 7-8.
%F A334445 A334445 / A334446 = 35*(PolyGamma(3, 1/4)/(8*Pi^4) - 1)/34.
%F A334445 A334445 * A334447 = 1680 / (17*Pi^4).
%e A334445 1.001649664033000425378578071929390888273984404386699300089837...
%Y A334445 Cf. A002144, A243380, A334424, A334449.
%K A334445 nonn,cons
%O A334445 1,5
%A A334445 _Vaclav Kotesovec_, Apr 30 2020
%E A334445 More digits from _Vaclav Kotesovec_, Jun 27 2020